Decentralised Random Competitive Dynamic Market Processes

We study a decentralised and uncoordinated market where heterogeneous self-interested firms and workers meet directly and randomly in pursuit of higher payoff over time. Each firm hires several workers and each worker has preferences over firms and salaries, taking at most one job. Neither firms nor workers possess perfect knowledge of the market. At any time any firm and any group of workers can form a new coalition if doing so makes no member of the coalition worse off and at least one member strictly better off. In this process, the firm may recruit workers from other firms and dismiss some of its own workers, the deserted firms and red workers can be worse off. This process is called the coalition improvement. We establish that starting from an arbitrary market state of a matching between firms and workers with a system of salaries, a decentralised random dynamic market process where each possible coalition improvement occurs with a positive probability converges with probability one to a competitive equilibrium, provided that an equilibrium exists. This theorem is built upon a crucial mathematical result which shows the existence of a nite sequence of successive coalition improvements from an arbitrary market state to equilibrium. Our results also have meaningful policy implications.